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 A004614 Numbers that are divisible only by primes congruent to 3 mod 4. 28
 1, 3, 7, 9, 11, 19, 21, 23, 27, 31, 33, 43, 47, 49, 57, 59, 63, 67, 69, 71, 77, 79, 81, 83, 93, 99, 103, 107, 121, 127, 129, 131, 133, 139, 141, 147, 151, 161, 163, 167, 171, 177, 179, 189, 191, 199, 201, 207, 209, 211, 213, 217, 223, 227, 231, 237, 239, 243, 249, 251 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Numbers whose factorization as Gaussian integers is the same as their factorization as integers. - Franklin T. Adams-Watters, Oct 14 2005 Closed under multiplication. Primitive elements are the primes of form 4*k+3. - Gerry Martens, Jun 17 2020 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 FORMULA Product(A079261(A027748(a(n),k)): k=1..A001221(a(n))) = 1. - Reinhard Zumkeller, Jan 07 2013 MATHEMATICA ok[1] = True; ok[n_] := And @@ (Mod[#, 4] == 3 &) /@ FactorInteger[n][[All, 1]]; Select[Range[251], ok] (* Jean-François Alcover, May 05 2011 *) A004614 = Select[Range[251], Length@Reduce[s^2 + t^2 == s # && s # > t > 0, Integers] == 0 &] (* Gerry Martens, Jun 05 2020 *) PROG (PARI) for(n=1, 1000, if(sumdiv(n, d, isprime(d)*if((d-3)%4, 1, 0))==0, print1(n, ", "))) (PARI) forstep(n=1, 999, 2, for(j=1, #t=factor(n)[, 1], t[j]%4==1 && next(2)); print1(n", ")) \\ M. F. Hasler, Feb 26 2008 (PARI) list(lim)=my(v=List([1]), cur, idx, newIdx); forprime(p=3, lim, if(p%4>1, listput(v, p))); for(i=2, #v, cur=v[i]; idx=1; while(v[idx]*cur <= lim, my(newidx=#v+1, t); for(j=idx, #v, t=cur*v[j]; if(t<=lim, listput(v, t))); idx=newidx)); Set(v) \\ Charles R Greathouse IV, Feb 06 2018 (Magma) [n: n in [1..300] | forall{d: d in PrimeDivisors(n) | d mod 4 eq 3}]; // Vincenzo Librandi, Aug 21 2012 (Haskell) a004614 n = a004614_list !! (n-1) a004614_list = filter (all (== 1) . map a079261 . a027748_row) [1..] -- Reinhard Zumkeller, Jan 07 2013 CROSSREFS Cf. A004613. Cf. A002145 (subsequence of primes). Sequence in context: A129747 A354570 A354039 * A112398 A197504 A167800 Adjacent sequences: A004611 A004612 A004613 * A004615 A004616 A004617 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified December 5 08:31 EST 2022. Contains 358584 sequences. (Running on oeis4.)